p-Adic Extension Leaves¶
The final classes for extensions of Zp and Qp (ie classes that are not just designed to be inherited from).
AUTHORS:
David Roe
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class
sage.rings.padics.padic_extension_leaves.EisensteinExtensionFieldCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric,sage.rings.padics.generic_nodes.pAdicCappedRelativeFieldGeneric
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class
sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedAbsolute(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation)¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric,sage.rings.padics.generic_nodes.pAdicCappedAbsoluteRingGeneric
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class
sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric,sage.rings.padics.generic_nodes.pAdicCappedRelativeRingGeneric
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class
sage.rings.padics.padic_extension_leaves.EisensteinExtensionRingFixedMod(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='NTL')¶ Bases:
sage.rings.padics.eisenstein_extension_generic.EisensteinExtensionGeneric,sage.rings.padics.generic_nodes.pAdicFixedModRingGeneric-
fraction_field()¶ Eisenstein extensions with fixed modulus do not support fraction fields.
EXAMPLES:
sage: S.<x> = ZZ[] sage: R.<a> = ZpFM(5).extension(x^2 - 5) sage: R.fraction_field() Traceback (most recent call last): ... TypeError: This implementation of the p-adic ring does not support fields of fractions.
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class
sage.rings.padics.padic_extension_leaves.UnramifiedExtensionFieldCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric,sage.rings.padics.generic_nodes.pAdicCappedRelativeFieldGeneric
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class
sage.rings.padics.padic_extension_leaves.UnramifiedExtensionFieldFloatingPoint(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric,sage.rings.padics.generic_nodes.pAdicFloatingPointFieldGeneric
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class
sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingCappedAbsolute(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric,sage.rings.padics.generic_nodes.pAdicCappedAbsoluteRingGeneric
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class
sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingCappedRelative(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric,sage.rings.padics.generic_nodes.pAdicCappedRelativeRingGeneric
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class
sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingFixedMod(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric,sage.rings.padics.generic_nodes.pAdicFixedModRingGeneric
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class
sage.rings.padics.padic_extension_leaves.UnramifiedExtensionRingFloatingPoint(exact_modulus, poly, prec, print_mode, shift_seed, names, implementation='FLINT')¶ Bases:
sage.rings.padics.unramified_extension_generic.UnramifiedExtensionGeneric,sage.rings.padics.generic_nodes.pAdicFloatingPointRingGeneric